problem archive
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3. If A and B are two sets such that A ⊆ B, then what is A ∪ B? -
4. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find (i) A ∪ B (ii) A ∪ C (iii) B ∪ C (iv) B ∪ D (v) A ∪ B ∪ C (vi) ... -
5. Find the intersection of each pair of sets of question 1 above. -
6. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (i) A ∩ B (ii) B ∩ C (iii) A ∩ C ∩ D (iv) B ∩ D (v) B ∩ D (vi)... -
If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, fin... -
Which of the following pairs of sets are disjoint (i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6} (ii) {a, e, i, o, u} and {c, d, e, f}... -
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find (i) A - B (ii) A - C (iii) A - D... -
If X = {a, b, c, d} and Y = {f, b, d, g}, find (i) X - Y (ii) Y - X (iii) X ∩ Y -
If R is the set of real numbers and Q is the set of rational numbers, then what is R - Q? -
State whether each of the following statement is true or false. Justify your answer. (i) {2, 3, 4, 5} and {3, 6} are disjoint sets. (ii) {a, e, i, o, ... -
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9}. Find A'. -
Let U be universal set of all the students of Class XI of a coeducational school and A be the set of all girls in Class XI. Find A'. -
Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}. Find A', B', A' ∩ B', A ∪ B and hence show that (A ∪ B)' = A' ∩ B'. -
Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4 }, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (i) A' (ii) B' (iii) (A ∪ C)' (iv) (A ∩ B)'... -
If U = { a, b, c, d, e, f, g, h }, find the complements of the following sets : (i) A = { a, b, c } (ii) B = { d, e, f, g } (iii) C = { a, c, e, g } (... -
Taking the set of natural numbers as the universal set, write down the complements of the following sets: (i) { x : x is an even natural number } (ii)... -
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that (i) (A ∪ B)' = A' ∩ B' (ii) (A ∩ B)' = A' ∪ B' -
Draw appropriate Venn diagram for each of the following : (i) (A ∪ B)', (ii) A' ∩ B', (iii) (A ∩ B)', (iv) A' ∪ B' -
Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A'? -
Fill in the blanks to make each of the following a true statement : (i) A ∪ A' = . . . (ii) ϕ' ∩ A = . . . (iii) A ∩ A' = . . . (iv) U' ∩ A = . . .